CIF: Small: Collaborative Research: Compressed Sensing for Coherent Designs under Gaussian/Non-Gaussian Noise

近年来，科学、工程和社会中的大量高维数据爆炸式增长，需要新的技术来从高维噪声观测中恢复稀疏信号。 为了解决这个问题，该项目旨在开发高效和鲁棒的方法来分析高维数据，这些方法在信号处理，通信，计算生物学，机器学习， 图像/视频编码、传感器网络、社会科学等。最近，压缩传感（CS）已经吸引了来自计算机科学、工程和统计学团体的大量关注。然而，CS恢复只有在特征弱相关时才有意义。单个异常值可能会完全破坏重建。计算过程不能满足的挑战，在统计精度，算法的稳定性和计算方便。 为了解决这些挑战，研究人员开发了新型的非凸正则化技术，以获得远远超出高斯性的相干统计模型的预测准确性和模型简约性。从理论上分析了它在估计、预测和稀疏恢复方面的性能。 提出了一类简单可行的算法，可用于求解任意非凸惩罚广义线性模型，并给出了一种对超高维数据进行非边缘特征筛选的随机化方法.此外，研究人员明确地研究了离群值的关键影响，并开发了一个强大的CS来处理高杠杆点和总离群值。统一的 框架 的 适用 到 小样本高维 问题 同时变量选择和离群值识别高斯/非高斯噪声。最后，该项目涉及丰富的激励性例子和广泛的应用，包括频谱分析，网络拓扑和动力学建模，图形模型，计算生物学，机器学习和图像压缩等各个领域，作为一个重要组成部分。

The recent explosion of large amounts of high dimensional data in science, engineering, and society demands new technologies to recover sparse signals from high dimensional noisy observations. To address it, this project aims to develop efficient and robust methods for analyzing high-dimensional data, which have wide applications in signal processing, communication, computational biology, machine learning, image/video coding, sensor networks, social science, etc.Recently, compressed sensing (CS) has attracted a good deal of attention from computer science, engineering, and statistics communities. However, the CS recovery only makes sense when the features are weakly correlated. A single rogue outlier may break down the reconstruction completely. The computational procedures cannot meet the challenge of ultrahigh dimensional problems in terms of statistical accuracy, algorithmic stability and computation expediency. To address these challenges, the investigators develop novel nonconvex regularization techniques to attain prediction accuracy and model parsimony for coherent statistical models that go much beyond Gaussianity. Theoretical analysis of its performance in estimation, prediction, and sparsity recovery is conducted. A class of simple algorithms feasible for solving essentially any nonconvex penalized generalized linear models is developed, together with a randomization technique of nonmarginal feature screening for ultra-high dimensional data. Furthermore, the investigators explicitly study the critical effects of outliers and develop a robust CS for handling high leverage points and gross outliers. A unified framework that applies to small-sample-size-high-dimension problems is provided for simultaneous variable selection and outlier identification under Gaussian/non-Gaussian noise. Finally, this project involves rich motivating examples and widespread applications in various areas including spectral analysis, network topology and dynamics modeling, graphical models, computational biology, machine learning, and image compression, as an essential component.